Question

A column ABC is supported at ends A and C and compressed by an axial load P (figure a). The column is fix-supported at the ends (support A and C). Lateral support is provided at point B but only in the plane ZX. The column is constructed of two channel sections (C6 * 10.5) (see figure). (Given: A=6.16 in?, Ix=30.2 in4, ly=16.14 in4, E = 29,500 ksi and oy = 50 ksi) 1. Determine the largest vertical force P that can be applied without causing buckling. 2. Compared the critical stress to the yield stress. 3. If the FS =3.0, what is the allowable value of load P. Z Р с 20 ft BK D

Answer 1

given ! C Leffective Qoft should take any two Joints pinned fixed B Le= 미의 oft A = 6.16 Inc? (Channel Area) Iy = 16.14 Inch't li Ia = 30.2 incht, E=29,500 ksi, oy= 50 ksi The largest vertical force that can be applied without causing Buckling is depends Minimum Area moment q Here Imin = Iy = 16.14 in 4 inestia T²E I min - Lez Euler Theory Peyfticas loced ²x x 29.500 x 16.14 e x 12,2 163.167 k pounds. Peri

critical stress Critical losed Area 163.167 6.16 26.488 ksi lyield stress => soksi Because The column is safest one is more yield stres More than the Yield stress is critical stress Material strength & Buckling stress stress Material will fail Bentore yield point of Materia). Factor of safety = 3.0 If 3 Loud p=2 allowable feritical load fos = Pallowable Load 2098 163 167 3. Pallowable = 54.389 kpounds Pallowble =

pallowable Based on yielding py oy= By = 50 K 6.16 Area Py = 308 kpounds By allow = 308 308 fos 3 102.6667K poun Pyallow Pallowable Based on critical Loued = 54.389 k pounds Pallow yield u 102.667K Pound Loud Material (column fail Before yield point)